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Complete asymptotic expansions for eigenvaluesofDirichlet Laplacian in thin three-dimensional rods*

Published online by Cambridge University Press:  06 August 2010

Denis Borisov
Affiliation:
Bashkir State Pedagogical University, October Revolution St. 3a, 450000 Ufa, Russia. [email protected]
Giuseppe Cardone
Affiliation:
University of Sannio, Department of Engineering, Corso Garibaldi, 107, 82100 Benevento, Italy. [email protected]
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Abstract

We consider the Dirichlet Laplacian in a thin curvedthree-dimensional rod. The rod is finite. Its cross-section isconstant and small, and rotates along the reference curve in anarbitrary way. We find a two-parametric set of the eigenvalues ofsuch operator and construct their complete asymptotic expansions. Weshow that this two-parametric set contains any prescribed number ofthe first eigenvalues of the considered operator. We obtain thecomplete asymptotic expansions for the eigenfunctions associatedwith these first eigenvalues.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2010

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